Kindergarten

## Third Grade Math Common Core State Standards and Curriculum

Third grade math standards take students down mathematical roads that are more complex and academically challenging. Before this point in a student’s education, they studied concepts that served the purpose as vital cornerstones for future math. Throughout third grade math, Common Core standards become slightly more demanding.

• Understanding of the Base Ten system
• The base ten system refers to place value. Students must have an understanding of place value and use it to solve problems. Common Core math standards for 3rd grade insist that they must have the ability to recognize groups within a number. For example, with the number 273, students must be able to recognize that the number can be broken down into 2 groups of 100, 7 groups of 10, and 3 groups of 1.
• Addition and Subtraction within 1000
• By the time your student enters third grade, they should have all single-digit, two-addend addition equations memorized. These include 1+1, 2+1, and so on up to 9+9. Students should also be able to add and subtract using mental strategies within 100. Common Core math standards, 3rd grade or otherwise, stress the importance of mental calculations. Students should be able to apply mental math and place value principles to solve problems involving only tens and hundreds. For example, they should not need to write down or count out problems similar to 100+50, 20+50, or 400+300.
• Fluency with Units of Measurement
• Students entering third grade should have practice measuring with standard units of measurement. They should also be familiar with word problems and real-word, physical examples of involving measurement. 3rd grade Common Core math standards takes these skills further and include inches and centimeters.
• Basic Geometry: Shapes and Characteristics
• By the end of second grade, students should be able to identify names and characteristics of basic shapes from memory. These include circle, triangle, square, rectangle, rhombus (or diamond), and heart. The characteristics of the shapes should also be remembered. For example, a student should understand that a square has four sides, and so does a rectangle. However, a rectangle does not have similar sides like a square does. Third grade Common Core Math Standards introduces this further.

### CCSS Math: 3rd Grade Study Tip

Ensure that your student gets plenty of math practice over the summer after second grade. They will need their skills to be sharp for the oncoming 3rd grade Common Core standards. Math success requires daily practice. To help incorporate math into your daily routine during summer vacation, ArgoPrep is the perfect place to start. The dreaded summer slide stops with ArgoPrep.

### 3rd Grade Common Core Math Standards: Four Focus Areas

In the third grade, students will spend most of their time in the classroom becoming familiar with four subjects. Despite some familiarity with some subjects, as well as the ability to draw from what they have already learned, these concepts are more complex than any previous subjects. Third grade presents challenges not seen previously and calls for flexible and resilient thinking.

#### Overview:

• Area 1) Introduction of Multiplication and Division
• Area 2) Fractions: Unit Fractions
• Area 3) Rectangular Arrays and Area
• Area 4) Analyzing Two-Dimensional Shapes
Though every new grade beings new subjects, third grade is particularly inundated with them. These subjects will be a part of all future math your student encounters. Mastery of these is just as important as mastery of addition and subtraction.

#### Study Tip:

Keep track of your student’s progress throughout the year and be aware of their strengths and weaknesses. Ask their teacher for assistance with this; they will be more than happy to help out. Keep a copy of a class syllabus handy. This will provide a scheduled list of topics your student will study. Additionally, while your student is doing homework or studying on ArgoPrep, make a note of the topics where they struggle the most. This will ensure that your student gets enough practice in the right areas.

### Common Core Standards Math: 3rd Grade Focus Area Breakdown and Study Suggestions

#### Area 1: Introduction of Multiplication and Division

Multiplication and division will be presented to your student and defined in the third grade. Multiplication will be defined as finding the product of an equation. This topic will be introduced through manipulating equal groups of objects. Physical examples and various illustrations will be used to represent numbers in equations. These groups will be small, such as 1x1, 2x3, and so on. This will create a multiplication basis to work from in the future. Students will utilize what they have learned in skip counting and number groups to develop multiplication skills. Division, not unlike multiplication, will be explained and developed with equal groups of objects to express numbers. It is defined as finding the quotient between two numbers. Division will be explained as the number form of the question, “How many groups of (number) are in (number)?” For example, students will develop an understanding that a division equation, such as 14÷2, is an expression of asking: “How many groups of 2 are in 14?”
##### Multiplication vs Division
Students will develop an understanding of the relationship between multiplication and division. This is something that third grade Common Core math standards requires. Understanding the two separately is only the first step. For example, your student may understand that 5x2=10. However, they must also understand that because of this, 10÷2=5. Students will also study that in multiplication, similarly to addition, the order of numbers in the equation comes out to the same product. This is called the commutative property of multiplication. For example, if 8x3=24, the commutative property suggests that 3x8 also equals 24. They must understand that despite their relationship, multiplication and division do not share the same properties.

#### Area 1 Study Suggestion:

When practicing multiplication at home, begin with small numbers. Using physical tools is helpful for tactical and visual learners. Take a group of beans, buttons, Lego bricks, or other small, like objects for this activity. Start out with a simple equation, such as 2x3. Create three groups of beans with two beans per group. Position the groups side by side. Guide students through writing out the equation. Explain that there are two beans, three times. Two times three. Try this method with different groups, such as two groups of three beans. When teaching division, begin with the aforementioned question. With the previous 2x3 beans equation, you can use 6÷2 as an example. “How many groups of 2 are in 6?” With a group of 6 beans, ask your student to count out 2 beans at a time. Once they have counted out 3 groups of 2 beans, return to the question. Ask them how many groups beans they have. Complete the equation with your student: 6÷2=3. Try this method with different equations, such as 6÷3, 8÷2, and so on. Tutorials are an excellent visual aid for students working to master Common Core math standards. Grade 3 math tutorials are available in ArgoPrep’s curriculum. The videos are thorough, interactive, and entertaining for your student to watch.

#### Area 2: Fractions: Unit Fractions

Fractions are one of the most abstract math concepts your students will learn throughout their development with Common Core standards. 3rd grade math studies surrounding fractions will be constituted largely of practice with unit fractions. Unit fractions are those with 1 as a numerator. In other words, they are fractions that represent only one part of the whole. For example. ⅕ is a unit fraction. It expresses 1 part of 5 total parts. However, ⅗ is not, as it expressed 3 parts of 5 total parts. To help visualize and work with fractions, number lines will be used to express them. Your student will most likely work with number lines from 0 to 1, with intervals showing fractions between them. For example, a student may work with a number line starting at 0 and continuing to 1 with intervals of ⅓. The first interval will represent ⅓. The next will represent ⅔. The final interval will represent 3/3, or 1. Students will develop their fraction comparison skills using physical examples. They will understand that ½ is larger than ⅓. This is because one piece of a ribbon cut into 2 pieces bigger than one piece of a ribbon cut into 3 pieces. In the same vein, ⅕ of a ribbon is smaller than ⅓ of a ribbon. This is because 1 piece of a ribbon cut into 5 pieces is smaller than 1 piece of a ribbon cut into 3 pieces.

#### Area 2 Study Suggestion

For teaching fractions, physical examples are the perfect way to begin. The aforementioned ribbon concept can be used as a real-world way to develop fraction understanding. Any easily divided object can be used. This includes cookies, cut paper, groups of the same object (beans, Lego bricks), or blocks. You can even use body parts. For example, you can refer to your student’s fingers to teach them the concept of ⅕ or 1/10. Using items they enjoy, or their own body, will interest them more than written numbers. Illustrations representing fractions, such as the ones found in ArgoPrep’s quality workbooks, are also extremely helpful tools.

#### Area 3: Rectangular Arrays and Area

During the third grade Common Core math standards will introduce students to the concept of area using rectangular shapes. They will learn how to find the area of a rectangular shape, and why this operation is possible. Students will understand the relationship that area has with multiplication and use it to draw conclusions about area and the shapes.

#### Area 3 Study Suggestion:

Students have likely used ten frames or base ten blocks before. You can use these again for teaching area, as they make the squared space easy to see. Explain that area can be found by multiplying the measurement of one side with the measurement of another. Measure a shape together and write out the correlating equation as you go along. Try this method with different rectangular shapes in drawings or in objects around your home.

#### Area 4: Analyzing Two-Dimensional Shapes

Geometry and shapes are an important part of third grade Common Core standards. Math surrounding geometry in this grade will focus not only on area, but on grouping shapes with similar attributes. Students will learn about the quadrilateral group of shapes, which are four-sided shapes with straight sides. Students will learn what shapes belong to this group, such as square, rectangle, trapezoid, and rhombus. They will also draw shapes that are quadrilaterals, but don’t fit any of the above names.

#### Area 4 Study Suggestion

Present your student with various shapes. They can be the basic ones mentioned above, or they can be more abstract. Ask students how many sides each shape has. Then, ask students to match up shapes with the same number of sides. Explain that shapes with 4 straight sides are called quadrilaterals. Hold up different shapes and ask your student if the shape is a quadrilateral. Try this method with different shapes found throughout your home.

## Operations & Algebraic Thinking

### Represent and solve problems involving multiplication and division.

#### CCSS.MATH.CONTENT.3.OA.A.1

Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each. For example, describe a context in which a total number of objects can be expressed as 5 × 7.

#### CCSS.MATH.CONTENT.3.OA.A.2

Interpret whole-number quotients of whole numbers, e.g., interpret 56 ÷ 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each. For example, describe a context in which a number of shares or a number of groups can be expressed as 56 ÷ 8.

#### CCSS.MATH.CONTENT.3.OA.A.3

Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.1

#### CCSS.MATH.CONTENT.3.OA.A.4

Determine the unknown whole number in a multiplication or division equation relating three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8 × ? = 48, 5 = _ ÷ 3, 6 × 6 = ?

### Understand properties of multiplication and the relationship between multiplication and division.

#### CCSS.MATH.CONTENT.3.OA.B.5

Apply properties of operations as strategies to multiply and divide.2 Examples: If 6 × 4 = 24 is known, then 4 × 6 = 24 is also known. (Commutative property of multiplication.) 3 × 5 × 2 can be found by 3 × 5 = 15, then 15 × 2 = 30, or by 5 × 2 = 10, then 3 × 10 = 30. (Associative property of multiplication.) Knowing that 8 × 5 = 40 and 8 × 2 = 16, one can find 8 × 7 as 8 × (5 + 2) = (8 × 5) + (8 × 2) = 40 + 16 = 56. (Distributive property.)

#### CCSS.MATH.CONTENT.3.OA.B.6

Understand division as an unknown-factor problem. For example, find 32 ÷ 8 by finding the number that makes 32 when multiplied by 8.

### Multiply and divide within 100.

#### CCSS.MATH.CONTENT.3.OA.C.7

Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers.

### Solve problems involving the four operations, and identify and explain patterns in arithmetic.

#### CCSS.MATH.CONTENT.3.OA.D.8

Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.3

#### CCSS.MATH.CONTENT.3.OA.D.9

Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. For example, observe that 4 times a number is always even, and explain why 4 times a number can be decomposed into two equal addends.

## Number & Operations in Base Ten

### Use place value understanding and properties of operations to perform multi-digit arithmetic.

#### CCSS.MATH.CONTENT.3.NBT.A.1

Use place value understanding to round whole numbers to the nearest 10 or 100.

#### CCSS.MATH.CONTENT.3.NBT.A.2

Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction.

#### CCSS.MATH.CONTENT.3.NBT.A.3

Multiply one-digit whole numbers by multiples of 10 in the range 10-90 (e.g., 9 × 80, 5 × 60) using strategies based on place value and properties of operations.

## Number & Operations—Fractions

### Develop understanding of fractions as numbers.

#### CCSS.MATH.CONTENT.3.NF.A.1

Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b.

#### CCSS.MATH.CONTENT.3.NF.A.2

Understand a fraction as a number on the number line; represent fractions on a number line diagram.
##### CCSS.MATH.CONTENT.3.NF.A.2.A
Represent a fraction 1/b on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts. Recognize that each part has size 1/b and that the endpoint of the part based at 0 locates the number 1/b on the number line.
##### CCSS.MATH.CONTENT.3.NF.A.2.B
Represent a fraction a/b on a number line diagram by marking off a lengths 1/b from 0. Recognize that the resulting interval has size a/b and that its endpoint locates the number a/b on the number line.

#### CCSS.MATH.CONTENT.3.NF.A.3

Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size.
##### CCSS.MATH.CONTENT.3.NF.A.3.A
Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line.
##### CCSS.MATH.CONTENT.3.NF.A.3.B
Recognize and generate simple equivalent fractions, e.g., 1/2 = 2/4, 4/6 = 2/3. Explain why the fractions are equivalent, e.g., by using a visual fraction model.
##### CCSS.MATH.CONTENT.3.NF.A.3.C
Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers. Examples: Express 3 in the form 3 = 3/1; recognize that 6/1 = 6; locate 4/4 and 1 at the same point of a number line diagram.
##### CCSS.MATH.CONTENT.3.NF.A.3.D
Compare two fractions with the same numerator or the same denominator by reasoning about their size. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.

## Measurement & Data

### Solve problems involving measurement and estimation.

#### CCSS.MATH.CONTENT.3.MD.A.1

Tell and write time to the nearest minute and measure time intervals in minutes. Solve word problems involving addition and subtraction of time intervals in minutes, e.g., by representing the problem on a number line diagram.

#### CCSS.MATH.CONTENT.3.MD.A.2

Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l).1 Add, subtract, multiply, or divide to solve one-step word problems involving masses or volumes that are given in the same units, e.g., by using drawings (such as a beaker with a measurement scale) to represent the problem.2

### Represent and interpret data.

#### CCSS.MATH.CONTENT.3.MD.B.3

Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step "how many more" and "how many less" problems using information presented in scaled bar graphs. For example, draw a bar graph in which each square in the bar graph might represent 5 pets.

#### CCSS.MATH.CONTENT.3.MD.B.4

Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by making a line plot, where the horizontal scale is marked off in appropriate units— whole numbers, halves, or quarters.

### Geometric measurement: understand concepts of area and relate area to multiplication and to addition.

#### CCSS.MATH.CONTENT.3.MD.C.5

Recognize area as an attribute of plane figures and understand concepts of area measurement.
##### CCSS.MATH.CONTENT.3.MD.C.5.A
A square with side length 1 unit, called "a unit square," is said to have "one square unit" of area, and can be used to measure area.
##### CCSS.MATH.CONTENT.3.MD.C.5.B
A plane figure which can be covered without gaps or overlaps by n unit squares is said to have an area of n square units.

#### CCSS.MATH.CONTENT.3.MD.C.6

Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units).

#### CCSS.MATH.CONTENT.3.MD.C.7

Relate area to the operations of multiplication and addition.
##### CCSS.MATH.CONTENT.3.MD.C.7.A
Find the area of a rectangle with whole-number side lengths by tiling it, and show that the area is the same as would be found by multiplying the side lengths.
##### CCSS.MATH.CONTENT.3.MD.C.7.B
Multiply side lengths to find areas of rectangles with whole-number side lengths in the context of solving real world and mathematical problems, and represent whole-number products as rectangular areas in mathematical reasoning.
##### CCSS.MATH.CONTENT.3.MD.C.7.C
Use tiling to show in a concrete case that the area of a rectangle with whole-number side lengths a and b + c is the sum of a × b and a × c. Use area models to represent the distributive property in mathematical reasoning.
##### CCSS.MATH.CONTENT.3.MD.C.7.D
Recognize area as additive. Find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts, applying this technique to solve real world problems.

### Geometric measurement: recognize perimeter.

#### CCSS.MATH.CONTENT.3.MD.D.8

Solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters.

## Geometry

### Reason with shapes and their attributes.

#### CCSS.MATH.CONTENT.3.G.A.1

Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories.

#### CCSS.MATH.CONTENT.3.G.A.2

Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole. For example, partition a shape into 4 parts with equal area, and describe the area of each part as 1/4 of the area of the shape.

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